The topological types of length bounded multicurves

TL;DR

This paper characterizes which topological types of multicurves on hyperbolic surfaces always have representatives satisfying certain length inequalities across all moduli space.

Contribution

It provides a topological classification of multicurves with length inequalities valid throughout moduli space, advancing understanding of hyperbolic surface geometry.

Findings

Identifies topological types with universal length inequalities

Provides criteria for length inequalities on multicurves

Enhances understanding of hyperbolic surface geometry

Abstract

This article discusses inequalities on lengths of curves on hyperbolic surfaces. In particular, a characterization is given of which topological types of curves and multicurves always have a representative that satisfies a length inequality that holds over all of moduli space.